Bezier curve conjugation for smooth curve joining and corner rounding
The authors propose an analytical method for the smooth connection of two Bezier curves of arbitrary degree using a connecting curve, which is also a Bezier curve. At the points of connection between the connecting curve and the original curves, the smoothness order corresponds to the degrees of...
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| Format: | Article |
| Language: | English |
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Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education
2025-06-01
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| Series: | Омский научный вестник |
| Subjects: | |
| Online Access: | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2025/%E2%84%962(194)/26-34%20%D0%9A%D1%80%D0%B8%D0%B2%D0%BE%D1%88%D0%B5%D0%B5%D0%B2%20%D0%9E.%20%D0%92.,%20%D0%9C%D0%B0%D0%B2%D1%80%D0%B8%D0%BD%20%D0%A1.%20%D0%92.,%20%D0%A1%D1%82%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D0%B0%20%D0%90.%20%D0%A1..pdf |
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| _version_ | 1839647296865697792 |
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| author | O. V. Krivosheev S. V. Mavrin A. S. Starkova |
| author_facet | O. V. Krivosheev S. V. Mavrin A. S. Starkova |
| author_sort | O. V. Krivosheev |
| collection | DOAJ |
| description | The authors propose an analytical method for the smooth connection of two Bezier curves of arbitrary
degree using a connecting curve, which is also a Bezier curve. At the points of connection between
the connecting curve and the original curves, the smoothness order corresponds to the degrees of
the original curves. Additional constraints can be imposed on the connecting curve, which frequently
arise when addressing practical design challenges. Theorems establishing the necessary conditions for
the existence of the connecting curve are proven. The capabilities of the proposed method are demonstrated
by solving two problems: the smooth connection of two initially given Bezier curves and the smooth rounding
of an interior corner formed by intersecting initially given Bezier curves. The solution to the second problem
enables both symmetric and asymmetric rounding of corners formed by the intersection of non-straight
lines, while maintaining a high degree of smoothness at the connection points. The influence of additional
constraints on the connecting curve's shape is shown. The proposed mathematical method is based on solving a system of linear equations, where the equations
represent the derivative equality conditions at the connection points and at the points where additional
constraints are applied. Bezier curves are treated as special cases of B-splines. The proposed method is
applicable to both 2D and 3D scenarios. |
| format | Article |
| id | doaj-art-88ad5f6d0c5640f38c7c1e95b39c9ee2 |
| institution | Matheson Library |
| issn | 1813-8225 2541-7541 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник |
| spelling | doaj-art-88ad5f6d0c5640f38c7c1e95b39c9ee22025-06-30T07:48:00ZengOmsk State Technical University, Federal State Autonoumos Educational Institution of Higher EducationОмский научный вестник1813-82252541-75412025-06-012 (194)263410.25206/1813-8225-2025-194-26-34Bezier curve conjugation for smooth curve joining and corner roundingO. V. Krivosheev0S. V. Mavrin1A. S. Starkova2Russian Federal Nuclear Center — All-Russian Research Institute of Experimental Physics; Sarov Institute of Physics and Technology — Branch of the National Research Nuclear University “MEPhI”Russian Federal Nuclear Center — All-Russian Research Institute of Experimental Physics; Sarov Institute of Physics and Technology — Branch of the National Research Nuclear University “MEPhI”Russian Federal Nuclear Center — All-Russian Research Institute of Experimental PhysicsThe authors propose an analytical method for the smooth connection of two Bezier curves of arbitrary degree using a connecting curve, which is also a Bezier curve. At the points of connection between the connecting curve and the original curves, the smoothness order corresponds to the degrees of the original curves. Additional constraints can be imposed on the connecting curve, which frequently arise when addressing practical design challenges. Theorems establishing the necessary conditions for the existence of the connecting curve are proven. The capabilities of the proposed method are demonstrated by solving two problems: the smooth connection of two initially given Bezier curves and the smooth rounding of an interior corner formed by intersecting initially given Bezier curves. The solution to the second problem enables both symmetric and asymmetric rounding of corners formed by the intersection of non-straight lines, while maintaining a high degree of smoothness at the connection points. The influence of additional constraints on the connecting curve's shape is shown. The proposed mathematical method is based on solving a system of linear equations, where the equations represent the derivative equality conditions at the connection points and at the points where additional constraints are applied. Bezier curves are treated as special cases of B-splines. The proposed method is applicable to both 2D and 3D scenarios.https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2025/%E2%84%962(194)/26-34%20%D0%9A%D1%80%D0%B8%D0%B2%D0%BE%D1%88%D0%B5%D0%B5%D0%B2%20%D0%9E.%20%D0%92.,%20%D0%9C%D0%B0%D0%B2%D1%80%D0%B8%D0%BD%20%D0%A1.%20%D0%92.,%20%D0%A1%D1%82%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D0%B0%20%D0%90.%20%D0%A1..pdfbezier curveparametric continuityconjugationcad-systemsgeometric kernelfull life cycle systems “sarus” |
| spellingShingle | O. V. Krivosheev S. V. Mavrin A. S. Starkova Bezier curve conjugation for smooth curve joining and corner rounding Омский научный вестник bezier curve parametric continuity conjugation cad-systems geometric kernel full life cycle systems “sarus” |
| title | Bezier curve conjugation for smooth curve joining and corner rounding |
| title_full | Bezier curve conjugation for smooth curve joining and corner rounding |
| title_fullStr | Bezier curve conjugation for smooth curve joining and corner rounding |
| title_full_unstemmed | Bezier curve conjugation for smooth curve joining and corner rounding |
| title_short | Bezier curve conjugation for smooth curve joining and corner rounding |
| title_sort | bezier curve conjugation for smooth curve joining and corner rounding |
| topic | bezier curve parametric continuity conjugation cad-systems geometric kernel full life cycle systems “sarus” |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2025/%E2%84%962(194)/26-34%20%D0%9A%D1%80%D0%B8%D0%B2%D0%BE%D1%88%D0%B5%D0%B5%D0%B2%20%D0%9E.%20%D0%92.,%20%D0%9C%D0%B0%D0%B2%D1%80%D0%B8%D0%BD%20%D0%A1.%20%D0%92.,%20%D0%A1%D1%82%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D0%B0%20%D0%90.%20%D0%A1..pdf |
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